Absolute Value Equations and Inequalities

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Presentation transcript:

Absolute Value Equations and Inequalities

Today's questions to answer... ~ What is the absolute value of a number? ~ How do we solve an absolute value equation? ~ How do we solve an absolute value inequality? ~ What are some real-world examples?

What is the absolute value of a number? ~The distance the number is from 0 on a number line. Written as...

Quick Example: So, what is the difference between and ? Determine the value of the following: So, what is the difference between and ?

REMEMBER, THE ABSOLUTE VALUE OF X AND -X ARE THE SAME! But what will happen when "x"is thrown into the mix? Suppose we have ******* where a,b, and c are real numbers and c>0. REMEMBER, THE ABSOLUTE VALUE OF X AND -X ARE THE SAME! What does that mean for c?

This is how we do it... When ******* We solve two problems...

Example 1) Solve ************

Try this on your own... *****

Let's change our signs... For parts a and b, try several numbers for "x"and see if you notice a pattern. a) b)

Absolute Value is less thAN... For ********************* an "and"compound inequality is created. So, this becomes... Absolute Value is great"OR" than For ****** an "or" compound inequality is created. So, this becomes...

Example 2) Solve Example 3) Solve

Try these on your own... 1) 2) ***

Pop Problem!!

Example 5) At the Brooks Graphic Company,the average starting salary for a new graphic designer is $37,600, but the actual salary could differ from the average by as much as $2590. a) Write an absolute value inequality to describe this situation. b) Solve the inequality to find the range of starting salaries.

Questions?